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- Min-max_theorem abstract "In linear algebra and functional analysis, the min-max theorem, or variational theorem, or Courant–Fischer–Weyl min-max principle, is a result that gives a variational characterization of eigenvalues of compact Hermitian operators on Hilbert spaces. It can be viewed as the starting point of many results of similar nature.This article first discusses the finite-dimensional case and its applications before considering compact operators on infinite-dimensional Hilbert spaces. We will see that for compact operators, the proof of the main theorem uses essentially the same idea from the finite-dimensional argument.In the case that the operator is non-Hermitian, the theorem provides an equivalent characterization of the associated singular values. The min-max theorem can be extended to self-adjoint operators that are bounded below.".
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- Min-max_theorem wikiPageWikiLink Category:Articles_containing_proofs.
- Min-max_theorem wikiPageWikiLink Category:Operator_theory.
- Min-max_theorem wikiPageWikiLink Category:Spectral_theory.
- Min-max_theorem wikiPageWikiLink Category:Theorems_in_functional_analysis.
- Min-max_theorem wikiPageWikiLink Cluster_point.
- Min-max_theorem wikiPageWikiLink Compact_operator_on_Hilbert_space.
- Min-max_theorem wikiPageWikiLink Compression_(functional_analysis).
- Min-max_theorem wikiPageWikiLink Courant_minimax_principle.
- Min-max_theorem wikiPageWikiLink Eigenvalues_and_eigenvectors.
- Min-max_theorem wikiPageWikiLink Essential_spectrum.
- Min-max_theorem wikiPageWikiLink Functional_analysis.
- Min-max_theorem wikiPageWikiLink Hermitian.
- Min-max_theorem wikiPageWikiLink Hermitian_matrix.
- Min-max_theorem wikiPageWikiLink Hilbert_space.
- Min-max_theorem wikiPageWikiLink Hilbert_spaces.
- Min-max_theorem wikiPageWikiLink Limit_point.
- Min-max_theorem wikiPageWikiLink Linear_algebra.
- Min-max_theorem wikiPageWikiLink List_of_things_named_after_Charles_Hermite.
- Min-max_theorem wikiPageWikiLink Max–min_inequality.
- Min-max_theorem wikiPageWikiLink Multiplicity_(mathematics).
- Min-max_theorem wikiPageWikiLink Rayleigh_quotient.
- Min-max_theorem wikiPageWikiLink Self-adjoint_operator.
- Min-max_theorem wikiPageWikiLink Singular_value.
- Min-max_theorem wikiPageWikiLink Singular_values.
- Min-max_theorem wikiPageWikiLink Spectrum_(functional_analysis).
- Min-max_theorem wikiPageWikiLinkText "Cauchy interlacing theorem".
- Min-max_theorem wikiPageWikiLinkText "Min-Max Theorem".
- Min-max_theorem wikiPageWikiLinkText "Min-max theorem".
- Min-max_theorem wikiPageWikiLinkText "min-max theorem".
- Min-max_theorem wikiPageWikiLinkText "variational interpretation of eigenvalues".
- Min-max_theorem wikiPageWikiLinkText "variational theorem".
- Min-max_theorem hasPhotoCollection Min-max_theorem.
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- Min-max_theorem wikiPageUsesTemplate Template:Math.
- Min-max_theorem wikiPageUsesTemplate Template:Mvar.
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- Min-max_theorem subject Category:Articles_containing_proofs.
- Min-max_theorem subject Category:Operator_theory.
- Min-max_theorem subject Category:Spectral_theory.
- Min-max_theorem subject Category:Theorems_in_functional_analysis.
- Min-max_theorem hypernym Result.
- Min-max_theorem type Article.
- Min-max_theorem type Article.
- Min-max_theorem type Function.
- Min-max_theorem type Proof.
- Min-max_theorem type Theorem.
- Min-max_theorem type Thing.
- Min-max_theorem comment "In linear algebra and functional analysis, the min-max theorem, or variational theorem, or Courant–Fischer–Weyl min-max principle, is a result that gives a variational characterization of eigenvalues of compact Hermitian operators on Hilbert spaces. It can be viewed as the starting point of many results of similar nature.This article first discusses the finite-dimensional case and its applications before considering compact operators on infinite-dimensional Hilbert spaces.".
- Min-max_theorem label "Min-max theorem".
- Min-max_theorem differentFrom Minimax.
- Min-max_theorem differentFrom Variational_principle.
- Min-max_theorem sameAs Satz_von_Courant-Fischer.
- Min-max_theorem sameAs Théorème_min-max.
- Min-max_theorem sameAs m.033fm1.
- Min-max_theorem sameAs Теорема_Куранта_—_Фишера.
- Min-max_theorem sameAs Q4454958.
- Min-max_theorem sameAs Q4454958.
- Min-max_theorem wasDerivedFrom Min-max_theorem?oldid=678093961.
- Min-max_theorem isPrimaryTopicOf Min-max_theorem.